Observing Student Communication
 Introduction | Problem: Folded-Square Shapes | Solution: Folded-Square Shapes | Problem Reflection #1 | Problem: Sorting Shapes | Solution: Sorting Shapes | Problem Reflection #2 | Classroom Practice | Observe a Classroom | Your Journal

Think about the student work and reflect on the following questions. After you formulate your answers, select "Show Answer" to compare them with our responses.

 Question: How does this activity help the teacher assess student knowledge and provide the student with an opportunity to communicate his or her understanding? Show Answer
 Our Answer: The teacher gains information on the depth of student understanding of shapes, such as triangles and hexagons. The activity gives the student control over what categories to think and write about. Additionally, when used within a group or class, the activity should provide a rich variety of ideas to discuss.
 Question: How does this activity elicit evidence of misunderstandings about geometric terms? Show Answer
 Our Answer: Tasks like this sorting activity provide opportunities for a teacher to discover students' misconceptions, such as a student's expectation that shapes must look like the examples that were seen when the shape names were learned. For example, Maria's response shows that she may believe that all sides must be the same length if the shape is called a pentagon or hexagon. Another student misconception may be thinking that a triangle must have a base parallel to the bottom of a page or screen. Activity like this provides an opportunity to work with students to resolve such misconceptions as figures are re-examined in light of standard definitions of such words as "triangle" and "pentagon." For instance, teacher questions can help a student consolidate his or her understanding of triangles or pentagons.
 Question: How might you follow up and use this activity to further clarify such terms as "triangle" and "pentagon"? Show Answer
 Our Answer: One way is to ask what makes a figure a triangle and to come to agreement on a definition that includes having three straight sides, three angles, and three corners or vertices. Figures that are obviously not triangles could then be eliminated. Careful counting could be used to identify less standard triangles, such as one that seems upside down or with an angle that is too small or too big.

When students are asked to create, sort and describe unfamiliar shapes, their understanding of formal vocabulary terms, such as "pentagon," "right angle," "edge" or "symmetric" is put to the test. Often, their comprehension expands to include a more accurate and complete understanding of such terms and the ideas behind them. Activities like this also offer valuable assessment information to the teacher as well as opportunities to follow up with additional clarifying discussions and activities.

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